heat transfer is awful simple stuff. If the sun is hitting that 3 inch aluminum shell, radiation is warming the metal up... and if the craft's skin is one piece, heat is spreading to the full skin, the bottom side doesn't stay cool... a tad cooler, but that's all. Heat is radiating back into space but that is insignificant compared to the heat being radiated into the metal by the sun. That is simple physics, not rocket science
Someone else on the internet, who works with metals, listed the 250 degrees as the temp that the Apollo aluminum skin would hold at. I didn't make that number up.
The Apollo cabin was pressurized, so heat transfer into the cabin from the metal skin via convection is a given.
The Apollo cabins had no cooling.
this is airtight, there's no way around it. Apollo missions would have cooked if they were real.